Preheat your oven to 210 degrees and line the base of a 20cm round cake tin with baking paper.
Peel and cut the apples into eighths.
Add the butter to a frying pan and warm over a medium to high heat before adding the apple pieces. Cook the apples for 4 - 5 minutes turning them every minute or two until they begin to turn a golden brown colour.
Remove the sheet of puff pastry from the freezer to allow it to thaw slightly before you need it.
Add the brown sugar and cinnamon along with 2 tablespoons of cold water.
Cook for a further 3 - 4minutes until the sugar has dissolved before reducing the heat to low and simmering for a further couple of minutes until the apples have turned a lovely dark brown.
Remove the frying pan from the heat and using tongs, carefully arrange the apple pieces over the base of the lined cake tin and spoon over the sugar syrup.
Cut a 22cm circle from the pastry and place it over the apples, carefully tucking the pastry edge in.
Place the cake tin into the oven and cook for 15 minutes or until the pastry has puffed up and has turned golden brown.
Remove the cake tin from the oven and allow the Apple Tarte Tatin to stand in the tin for 5 minutes before carefully turning it onto a plate to serve.